A theory of idealized balloon flight dynamics is developed for the case of a rigidly suspended payload. A system of dynamical equations is deduced from Newton’s second law for translation and rotation. Linear perturbation theory is used to study the small oscillations of the balloon system. It is proved that the horizontal and angular degrees of freedom are coupled, while the vertical degree is independent. A cubic secular equation is derived for the complex frequency of the motion. For the case of light damping and coupling, it is shown that the frequency is determined only by inertial and geometric factors. Physical arguments are used to elucidate the mechanism of linear coupling and damping. Finally, it is shown that the second‐order vertical velocity perturbation is driven by the angular oscillation at a frequency twice as great.